Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 8 - Potential Energy and Conservation of Energy - Problems: 10b

Answer

the speed will not change

Work Step by Step

The total Energy of the book at the top of the building is: $E_{tot}=E_{k0}+E_{p0}=0+mgH(1)$ since book doesn't have initial speed So when student catches the book the total energy of the book will be: $E_{tot}=E_{k1}+E_{p1}=\dfrac {mv^{2}_{1}}{2}+mgh\left( 2\right) $ where H is the height of the building and h is the height relative to the ground that student catches the book so from (1) and (2) we get: $E_{tot}=E_{k1}+E_{p01}=\dfrac {mv^{2}_{1}}{2}+mgh=mgH\Rightarrow v_{1}=\sqrt {2g\left( H-h\right) }$ As you see speed doesn't belong mass ( there is no m in this equation) so the speed will not change
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